Reliable uncertainty quantification is a central challenge in kinetic plasma simulation, where high dimensionality, multiple physical scales, and sensitivity to uncertain inputs make repeated high-fidelity computations prohibitively expensive. This is particularly relevant in fusion-oriented applications, for which accurate predictions require sophisticated numerical solvers but direct sampling is often out of reach.

In this talk, I will present a multifidelity framework for the Vlasov–Poisson–Landau system designed to combine, rather than replace, high-order numerical simulation with machine learning. At the high-fidelity level, asymptotic-preserving and structure-aware solvers provide accurate kinetic descriptions across different regimes. These are coupled with reduced plasma models and tensor neural surrogates constructed through a micro–macro decomposition, so that the dominant physical structure is treated analytically and numerically, while learning is used only for the lower-complexity kinetic correction.  The resulting hierarchy produces inexpensive low-fidelity samples that remain strongly correlated with the high-fidelity kinetic solution.  When used as control variates, these models yield substantial variance reduction and computational savings while retaining the high-order solver as the reference description.

Beyond the specific plasma application, the main message is that classical numerical analysis and machine learning need not be competing approaches. High-order solvers can provide structure, reliability, and asymptotic consistency, while learned models provide efficient approximations that can be exploited within rigorous multifidelity estimators. This interaction offers a general route toward trustworthy machine learning for computational science.
 

In this talk, we study some Prandtl-type boundary layer models, including the two-dimensional MHD boundary layer equations and the Prandtl–Shercliff model. For small perturbations of a tangential background magnetic field, we establish the global-in-time existence and uniqueness of solutions to the MHD boundary layer equations in Sobolev spaces. The proof relies on a novel combination of the well-known cancellation mechanism and the concept of linearly good unknowns. We also investigate the Prandtl–Shercliff model. In the two-dimensional case, we establish global-in-time well-posedness in Sobolev spaces without imposing any structural assumptions on the initial data. Moreover, we show that solutions exhibit a global analytic regularization effect in all variables, up to the boundary and for all times. The proofs rely crucially on the intrinsic nonlocal diffusion induced by the Shercliff boundary layer.